Export as .obj and .jpg
When you want to export an obj file with jpeg textures, simply create jpg textures first. 

*.mtl is no image format. A Obj file is made of two parts. The *.obj part contains the mesh data. The *.mtl part contains material settings for a primitive phong shader, including the texture paths. You should not leave the *.mtl part away, it is part of the obj file. And when you leave it away then the textures are not found.

So when you export an obj file with jpg textures, then you should end in three parts. The *.obj file, the *.mtl file, and the *.jpg file.

(As a side note, Jpg is the worst texture format you can choose. It uses a lossy compression. You loose quality. I prefer PNG)